Question

a cone and a cylinder have the same radius and height. if the cylinders volume is ( 600pi cm^{3} ), what is the cones volume?
a. ( 300pi cm^{3} )
b. ( 100pi cm^{3} )
c. ( 200pi cm^{3} )
d. ( 600pi cm^{3} )

Explanation:

Step1: Recall the volume formulas

Volume of a cylinder \(V_{cylinder}=\pi r^{2}h\). Volume of a cone \(V_{cone}=\frac{1}{3}\pi r^{2}h\).

Step2: Use the relationship

Since the cone and cylinder have the same radius \(r\) and height \(h\), and \(V_{cylinder}=\pi r^{2}h = 600\pi\). Then \(V_{cone}=\frac{1}{3}V_{cylinder}\).

Step3: Calculate the cone's volume

Substitute \(V_{cylinder}=600\pi\) into the formula for \(V_{cone}\). \(V_{cone}=\frac{1}{3}\times600\pi = 200\pi\).

Answer:

C. \(200\pi \text{ cm}^3\)